Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 10 to 5 computations (50% saved)

sample726.0ms (23.2%)

Results

697.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 14 computations (51.7% saved)

simplify8.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
2×	`associate-r_binary64`
2×	`count-2_binary64`
1×	`associate-l_binary64`
1×	`distribute-rgt-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	4
1	11	4
2	14	4
3	17	4

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(hypot.f64 x x)

Compiler

Compiled 20 to 9 computations (55% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(hypot.f64 x x)

series4.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(hypot.f64 x x)

rewrite28.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

249×	`log1p-expm1-u_binary64`
249×	`expm1-log1p-u_binary64`
230×	`add-cbrt-cube_binary64`
227×	`add-cube-cbrt_binary64`
222×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4
1	60	4
2	700	4

Stop Event

1×	node limit

Counts

1 → 40

Calls

1 calls:

27.0ms

(hypot.f64 x x)

simplify12.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	80
1	12	80
2	25	80
3	29	80
4	33	80
5	51	80
6	73	80
7	84	80
8	96	80
9	121	80

Stop Event

1×

saturated

Counts

52 → 43

prune23.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	37	6	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	7	44

Error

0.0b

Counts

44 → 7

Alt Table

Status	Error	Program
	34.6b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
▶	1.4b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
	29.1b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	34.0b	(*.f64 (sqrt.f64 2) x)
✓	0.1b	(hypot.f64 x x)
	44.9b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	2.2b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 3) (cbrt.f64 (hypot.f64 x x)))

Compiler

Compiled 497 to 241 computations (51.5% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(hypot.f64 x x)
✓	0.3b	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
✓	0.6b	(cbrt.f64 (hypot.f64 x x))

series361.0ms (11.5%)

Counts

3 → 36

Calls

3 calls:

181.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
177.0ms	(cbrt.f64 (hypot.f64 x x))
4.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))

rewrite44.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

439×	`log1p-expm1-u_binary64`
439×	`expm1-log1p-u_binary64`
333×	`unpow-prod-down_binary64`
224×	`log-prod_binary64`
131×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	142	19
2	1333	19

Stop Event

1×	node limit

Counts

3 → 121

Calls

3 calls:

41.0ms	(*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (hypot.f64 x x)) 2))
41.0ms	(pow.f64 (cbrt.f64 (hypot.f64 x x)) 2)
41.0ms	(cbrt.f64 (hypot.f64 x x))

simplify42.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

427×	`associate-l_binary64`
423×	`fma-neg_binary64`
337×	`associate-r_binary64`
281×	`fma-def_binary64`
276×	`unswap-sqr_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	27	500
1	67	500
2	144	452
3	371	332
4	1203	324
5	4386	324

Stop Event

1×	node limit

Counts

157 → 134

prune135.0ms (4.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	281	2	283
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	282	8	290

Error

Counts

290 → 8

Alt Table

Status	Error	Program
	34.6b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	29.1b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	34.0b	(*.f64 (sqrt.f64 2) x)
	2.9b	(.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 2) 3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 2))
✓	0.1b	(hypot.f64 x x)
▶	1.8b	(.f64 (cbrt.f64 (hypot.f64 x x)) (.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	44.9b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
	2.2b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 3) (cbrt.f64 (hypot.f64 x x)))

Compiler

Compiled 5085 to 2051 computations (59.7% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))
✓	0.6b	(pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)
	0.6b	(cbrt.f64 (hypot.f64 x x))
✓	0.6b	(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))

series646.0ms (20.6%)

Counts

3 → 36

Calls

3 calls:

258.0ms

(*.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))

217.0ms

(pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)

170.0ms

(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))

rewrite48.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

629×	`log1p-expm1-u_binary64`
629×	`expm1-log1p-u_binary64`
359×	`log-prod_binary64`
131×	`expm1-udef_binary64`
131×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	179	28
2	1937	28

Stop Event

1×	node limit

Counts

3 → 67

Calls

3 calls:

46.0ms

(*.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x))))

46.0ms

(pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)

46.0ms

(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))

simplify36.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

747×	`fma-def_binary64`
322×	`unswap-sqr_binary64`
244×	`exp-sum_binary64`
188×	`exp-prod_binary64`
151×	`sqr-pow_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	40	660
1	106	528
2	244	516
3	657	468
4	2199	444

Stop Event

1×	node limit

Counts

103 → 79

prune165.0ms (5.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	363	0	363
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	363	8	371

Error

Counts

371 → 8

Alt Table

Status	Error	Program
	34.6b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	29.1b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	34.0b	(*.f64 (sqrt.f64 2) x)
	2.9b	(.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 2) 3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 2))
✓	0.1b	(hypot.f64 x x)
✓	1.8b	(.f64 (cbrt.f64 (hypot.f64 x x)) (.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	44.9b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
▶	2.2b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 3) (cbrt.f64 (hypot.f64 x x)))

Compiler

Compiled 10862 to 3693 computations (66% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)
	0.6b	(cbrt.f64 (hypot.f64 x x))
	0.6b	(cbrt.f64 (cbrt.f64 (hypot.f64 x x)))
✓	0.7b	(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 3)

series187.0ms (6%)

Counts

1 → 12

Calls

1 calls:

187.0ms

(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 3)

rewrite34.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

624×	`log1p-expm1-u_binary64`
624×	`expm1-log1p-u_binary64`
305×	`log-prod_binary64`
128×	`expm1-udef_binary64`
128×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	185	9
2	1892	9

Stop Event

1×	node limit

Counts

1 → 29

Calls

1 calls:

33.0ms

(pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 3)

simplify42.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

404×	`prod-exp_binary64`
324×	`*-commutative_binary64`
245×	`fma-neg_binary64`
218×	`exp-sum_binary64`
217×	`fma-def_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	26	228
1	59	228
2	123	228
3	332	228
4	1328	228
5	3457	192

Stop Event

1×	node limit

Counts

41 → 34

prune101.0ms (3.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	218	8	226

Error

Counts

226 → 8

Alt Table

Status	Error	Program
	34.6b	(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 x x) 1/2))
	29.1b	(*.f64 (sqrt.f64 2) (neg.f64 x))
	34.0b	(*.f64 (sqrt.f64 2) x)
	2.9b	(.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 2) 3) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))) 2))
✓	0.1b	(hypot.f64 x x)
✓	1.8b	(.f64 (cbrt.f64 (hypot.f64 x x)) (.f64 (*.f64 (cbrt.f64 (hypot.f64 x x)) (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2)) (cbrt.f64 (cbrt.f64 (hypot.f64 x x)))))
	44.9b	(cbrt.f64 (pow.f64 (hypot.f64 x x) 3))
✓	2.2b	(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (hypot.f64 x x))) 2) 3) (cbrt.f64 (hypot.f64 x x)))

Compiler

Compiled 4627 to 2218 computations (52.1% saved)

regimes354.0ms (11.3%)

Accuracy

Total 0.1b remaining (74.9%)

Threshold costs 0.1b (74.9%)

Counts

103 → 1

Compiler

Compiled 6394 to 3892 computations (39.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3	4

Stop Event

1×

saturated

end97.0ms (3.1%)

Compiler: Compiled 102 to 57 computations (44.1% saved)

Details

analyze4.0ms (0.1%)

sample726.0ms (23.2%)

simplify8.0ms (0.3%)

prune3.0ms (0.1%)

localize2.0ms (0.1%)

series4.0ms (0.1%)

rewrite28.0ms (0.9%)

simplify12.0ms (0.4%)

prune23.0ms (0.7%)

localize6.0ms (0.2%)

series361.0ms (11.5%)

rewrite44.0ms (1.4%)

simplify42.0ms (1.3%)

prune135.0ms (4.3%)

localize10.0ms (0.3%)

series646.0ms (20.6%)

rewrite48.0ms (1.5%)

simplify36.0ms (1.2%)

prune165.0ms (5.3%)

localize10.0ms (0.3%)

series187.0ms (6%)

rewrite34.0ms (1.1%)

simplify42.0ms (1.3%)

prune101.0ms (3.2%)

regimes354.0ms (11.3%)

simplify2.0ms (0.1%)

end97.0ms (3.1%)

Profiling